 
(* ::Section:: *)
(* Series2 *)
(* ::Text:: *)
(*Series2 performs a series expansion around 0. Series2 is (up to the Gamma-bug in Mathematica versions smaller than 5.0) equivalent to Series, except that it applies Normal on the result and has an option FinalSubstitutions. Series2[f, e, n] is equivalent to Series2[f, {e, 0, n}]..*)


(* ::Subsection:: *)
(* Examples *)
Series2[(x (1-x))^(\[Delta]/2),\[Delta],1]

Series2[Gamma[x],x,1]

Series[Gamma[x],{x,0,1}]

Series2[Gamma[x],x,2]

Series2[Gamma[x],x,2,FinalSubstitutions->{}]//FullSimplify

Series[Gamma[x],{x,0,If[$VersionNumber<5,4,2]}]//Normal//Expand//FullSimplify


(* ::Text:: *)
(*There is a table of expansions of special hypergeometric functions.*)


Series2[HypergeometricPFQ[{1,OPEm-1,Epsilon/2+OPEm},{OPEm,OPEm+Epsilon},1],Epsilon,1]

 Series2[HypergeometricPFQ[{1, OPEm, Epsilon/2 + OPEm}, {1 + OPEm, Epsilon + OPEm},  1],Epsilon,1]

Hypergeometric2F1[1, Epsilon, 1 + 2 Epsilon,x]

Series2[%,Epsilon,3]


(* ::Text:: *)
(*There are over 100 more special expansions of $, text{}_2F_1$ tabulated in Series2.m. The interested user can consult the source code (search for HYPERLIST).*)

